Properties

Label 1728.3.q.e.449.1
Level $1728$
Weight $3$
Character 1728.449
Analytic conductor $47.085$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1728.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(47.0845896815\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 449.1
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1728.449
Dual form 1728.3.q.e.1601.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.39898 - 1.96240i) q^{5} +(-6.39898 - 11.0834i) q^{7} +O(q^{10})\) \(q+(-3.39898 - 1.96240i) q^{5} +(-6.39898 - 11.0834i) q^{7} +(-14.2980 + 8.25493i) q^{11} +(-1.39898 + 2.42310i) q^{13} +2.54270i q^{17} -21.5959 q^{19} +(-2.60102 - 1.50170i) q^{23} +(-4.79796 - 8.31031i) q^{25} +(-13.1969 + 7.61926i) q^{29} +(13.6010 - 23.5577i) q^{31} +50.2295i q^{35} +10.4041 q^{37} +(34.5000 + 19.9186i) q^{41} +(17.0959 + 29.6110i) q^{43} +(-58.1969 + 33.6000i) q^{47} +(-57.3939 + 99.4091i) q^{49} -100.680i q^{53} +64.7980 q^{55} +(5.29796 + 3.05878i) q^{59} +(20.3990 + 35.3321i) q^{61} +(9.51021 - 5.49072i) q^{65} +(54.4898 - 94.3791i) q^{67} -52.8829i q^{71} +68.7878 q^{73} +(182.985 + 105.646i) q^{77} +(12.7929 + 22.1579i) q^{79} +(52.0857 - 30.0717i) q^{83} +(4.98979 - 8.64258i) q^{85} +7.62809i q^{89} +35.8082 q^{91} +(73.4041 + 42.3799i) q^{95} +(50.7020 + 87.8185i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 6q^{5} - 6q^{7} + O(q^{10}) \) \( 4q + 6q^{5} - 6q^{7} - 18q^{11} + 14q^{13} - 8q^{19} - 30q^{23} + 20q^{25} + 6q^{29} + 74q^{31} + 120q^{37} + 138q^{41} - 10q^{43} - 174q^{47} - 112q^{49} + 220q^{55} - 18q^{59} + 62q^{61} + 234q^{65} + 22q^{67} + 40q^{73} + 438q^{77} - 86q^{79} - 66q^{83} - 176q^{85} + 300q^{91} + 372q^{95} + 242q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(703\) \(1217\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −3.39898 1.96240i −0.679796 0.392480i 0.119982 0.992776i \(-0.461716\pi\)
−0.799778 + 0.600296i \(0.795050\pi\)
\(6\) 0 0
\(7\) −6.39898 11.0834i −0.914140 1.58334i −0.808156 0.588969i \(-0.799534\pi\)
−0.105984 0.994368i \(-0.533799\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −14.2980 + 8.25493i −1.29981 + 0.750448i −0.980372 0.197157i \(-0.936829\pi\)
−0.319443 + 0.947606i \(0.603496\pi\)
\(12\) 0 0
\(13\) −1.39898 + 2.42310i −0.107614 + 0.186393i −0.914803 0.403900i \(-0.867654\pi\)
0.807189 + 0.590293i \(0.200988\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.54270i 0.149570i 0.997200 + 0.0747852i \(0.0238271\pi\)
−0.997200 + 0.0747852i \(0.976173\pi\)
\(18\) 0 0
\(19\) −21.5959 −1.13663 −0.568314 0.822812i \(-0.692404\pi\)
−0.568314 + 0.822812i \(0.692404\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.60102 1.50170i −0.113088 0.0652913i 0.442389 0.896823i \(-0.354131\pi\)
−0.555477 + 0.831532i \(0.687464\pi\)
\(24\) 0 0
\(25\) −4.79796 8.31031i −0.191918 0.332412i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −13.1969 + 7.61926i −0.455067 + 0.262733i −0.709968 0.704234i \(-0.751290\pi\)
0.254901 + 0.966967i \(0.417957\pi\)
\(30\) 0 0
\(31\) 13.6010 23.5577i 0.438743 0.759924i −0.558850 0.829269i \(-0.688757\pi\)
0.997593 + 0.0693442i \(0.0220907\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 50.2295i 1.43513i
\(36\) 0 0
\(37\) 10.4041 0.281191 0.140596 0.990067i \(-0.455098\pi\)
0.140596 + 0.990067i \(0.455098\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 34.5000 + 19.9186i 0.841463 + 0.485819i 0.857761 0.514048i \(-0.171855\pi\)
−0.0162980 + 0.999867i \(0.505188\pi\)
\(42\) 0 0
\(43\) 17.0959 + 29.6110i 0.397579 + 0.688628i 0.993427 0.114470i \(-0.0365170\pi\)
−0.595847 + 0.803098i \(0.703184\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −58.1969 + 33.6000i −1.23823 + 0.714894i −0.968733 0.248106i \(-0.920192\pi\)
−0.269500 + 0.963000i \(0.586858\pi\)
\(48\) 0 0
\(49\) −57.3939 + 99.4091i −1.17130 + 2.02876i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 100.680i 1.89963i −0.312810 0.949816i \(-0.601270\pi\)
0.312810 0.949816i \(-0.398730\pi\)
\(54\) 0 0
\(55\) 64.7980 1.17814
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5.29796 + 3.05878i 0.0897959 + 0.0518437i 0.544226 0.838939i \(-0.316824\pi\)
−0.454430 + 0.890783i \(0.650157\pi\)
\(60\) 0 0
\(61\) 20.3990 + 35.3321i 0.334409 + 0.579214i 0.983371 0.181607i \(-0.0581298\pi\)
−0.648962 + 0.760821i \(0.724796\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 9.51021 5.49072i 0.146311 0.0844726i
\(66\) 0 0
\(67\) 54.4898 94.3791i 0.813281 1.40864i −0.0972755 0.995257i \(-0.531013\pi\)
0.910556 0.413386i \(-0.135654\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 52.8829i 0.744830i −0.928066 0.372415i \(-0.878530\pi\)
0.928066 0.372415i \(-0.121470\pi\)
\(72\) 0 0
\(73\) 68.7878 0.942298 0.471149 0.882054i \(-0.343839\pi\)
0.471149 + 0.882054i \(0.343839\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 182.985 + 105.646i 2.37642 + 1.37203i
\(78\) 0 0
\(79\) 12.7929 + 22.1579i 0.161935 + 0.280479i 0.935563 0.353161i \(-0.114893\pi\)
−0.773628 + 0.633640i \(0.781560\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 52.0857 30.0717i 0.627539 0.362310i −0.152260 0.988341i \(-0.548655\pi\)
0.779798 + 0.626031i \(0.215322\pi\)
\(84\) 0 0
\(85\) 4.98979 8.64258i 0.0587035 0.101677i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.62809i 0.0857089i 0.999081 + 0.0428545i \(0.0136452\pi\)
−0.999081 + 0.0428545i \(0.986355\pi\)
\(90\) 0 0
\(91\) 35.8082 0.393496
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 73.4041 + 42.3799i 0.772675 + 0.446104i
\(96\) 0 0
\(97\) 50.7020 + 87.8185i 0.522701 + 0.905345i 0.999651 + 0.0264148i \(0.00840908\pi\)
−0.476950 + 0.878931i \(0.658258\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.19694 + 0.691053i −0.0118509 + 0.00684211i −0.505914 0.862584i \(-0.668845\pi\)
0.494063 + 0.869426i \(0.335511\pi\)
\(102\) 0 0
\(103\) 0.792856 1.37327i 0.00769763 0.0133327i −0.862151 0.506652i \(-0.830883\pi\)
0.869849 + 0.493319i \(0.164216\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 103.223i 0.964702i −0.875978 0.482351i \(-0.839783\pi\)
0.875978 0.482351i \(-0.160217\pi\)
\(108\) 0 0
\(109\) −14.4041 −0.132148 −0.0660738 0.997815i \(-0.521047\pi\)
−0.0660738 + 0.997815i \(0.521047\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 92.0755 + 53.1598i 0.814828 + 0.470441i 0.848630 0.528988i \(-0.177428\pi\)
−0.0338020 + 0.999429i \(0.510762\pi\)
\(114\) 0 0
\(115\) 5.89388 + 10.2085i 0.0512511 + 0.0887695i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 28.1816 16.2707i 0.236820 0.136728i
\(120\) 0 0
\(121\) 75.7878 131.268i 0.626345 1.08486i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 135.782i 1.08626i
\(126\) 0 0
\(127\) −183.980 −1.44866 −0.724329 0.689454i \(-0.757850\pi\)
−0.724329 + 0.689454i \(0.757850\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −91.6918 52.9383i −0.699938 0.404109i 0.107387 0.994217i \(-0.465752\pi\)
−0.807324 + 0.590108i \(0.799085\pi\)
\(132\) 0 0
\(133\) 138.192 + 239.355i 1.03904 + 1.79966i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 165.288 95.4289i 1.20648 0.696562i 0.244491 0.969651i \(-0.421379\pi\)
0.961989 + 0.273090i \(0.0880457\pi\)
\(138\) 0 0
\(139\) −47.4898 + 82.2547i −0.341653 + 0.591761i −0.984740 0.174033i \(-0.944320\pi\)
0.643087 + 0.765793i \(0.277653\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 46.1939i 0.323034i
\(144\) 0 0
\(145\) 59.8082 0.412470
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 79.6112 + 45.9636i 0.534304 + 0.308480i 0.742767 0.669550i \(-0.233513\pi\)
−0.208464 + 0.978030i \(0.566846\pi\)
\(150\) 0 0
\(151\) 8.20714 + 14.2152i 0.0543519 + 0.0941403i 0.891921 0.452191i \(-0.149357\pi\)
−0.837569 + 0.546331i \(0.816024\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −92.4592 + 53.3813i −0.596511 + 0.344396i
\(156\) 0 0
\(157\) −105.985 + 183.571i −0.675062 + 1.16924i 0.301389 + 0.953501i \(0.402550\pi\)
−0.976451 + 0.215740i \(0.930784\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 38.4374i 0.238742i
\(162\) 0 0
\(163\) −172.788 −1.06005 −0.530024 0.847983i \(-0.677817\pi\)
−0.530024 + 0.847983i \(0.677817\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 163.197 + 94.2218i 0.977227 + 0.564202i 0.901432 0.432921i \(-0.142517\pi\)
0.0757953 + 0.997123i \(0.475850\pi\)
\(168\) 0 0
\(169\) 80.5857 + 139.579i 0.476839 + 0.825909i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 52.1969 30.1359i 0.301716 0.174196i −0.341497 0.939883i \(-0.610934\pi\)
0.643214 + 0.765687i \(0.277601\pi\)
\(174\) 0 0
\(175\) −61.4041 + 106.355i −0.350880 + 0.607743i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 72.7108i 0.406205i 0.979157 + 0.203103i \(0.0651025\pi\)
−0.979157 + 0.203103i \(0.934897\pi\)
\(180\) 0 0
\(181\) 97.5959 0.539204 0.269602 0.962972i \(-0.413108\pi\)
0.269602 + 0.962972i \(0.413108\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −35.3633 20.4170i −0.191153 0.110362i
\(186\) 0 0
\(187\) −20.9898 36.3554i −0.112245 0.194414i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −282.560 + 163.136i −1.47937 + 0.854116i −0.999727 0.0233462i \(-0.992568\pi\)
−0.479645 + 0.877462i \(0.659235\pi\)
\(192\) 0 0
\(193\) −10.5102 + 18.2042i −0.0544570 + 0.0943223i −0.891969 0.452097i \(-0.850676\pi\)
0.837512 + 0.546419i \(0.184009\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 32.5413i 0.165184i 0.996583 + 0.0825922i \(0.0263199\pi\)
−0.996583 + 0.0825922i \(0.973680\pi\)
\(198\) 0 0
\(199\) −62.0000 −0.311558 −0.155779 0.987792i \(-0.549789\pi\)
−0.155779 + 0.987792i \(0.549789\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 168.894 + 97.5109i 0.831990 + 0.480349i
\(204\) 0 0
\(205\) −78.1765 135.406i −0.381349 0.660516i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 308.778 178.273i 1.47740 0.852980i
\(210\) 0 0
\(211\) −84.2980 + 146.008i −0.399516 + 0.691983i −0.993666 0.112372i \(-0.964155\pi\)
0.594150 + 0.804354i \(0.297489\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 134.196i 0.624169i
\(216\) 0 0
\(217\) −348.131 −1.60429
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6.16122 3.55718i −0.0278788 0.0160958i
\(222\) 0 0
\(223\) 78.1867 + 135.423i 0.350613 + 0.607280i 0.986357 0.164620i \(-0.0526399\pi\)
−0.635744 + 0.771900i \(0.719307\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 86.6510 50.0280i 0.381723 0.220388i −0.296845 0.954926i \(-0.595934\pi\)
0.678567 + 0.734538i \(0.262601\pi\)
\(228\) 0 0
\(229\) −104.995 + 181.856i −0.458493 + 0.794133i −0.998882 0.0472824i \(-0.984944\pi\)
0.540389 + 0.841416i \(0.318277\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 307.127i 1.31814i 0.752081 + 0.659070i \(0.229050\pi\)
−0.752081 + 0.659070i \(0.770950\pi\)
\(234\) 0 0
\(235\) 263.747 1.12233
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 70.3888 + 40.6390i 0.294514 + 0.170038i 0.639976 0.768395i \(-0.278944\pi\)
−0.345462 + 0.938433i \(0.612278\pi\)
\(240\) 0 0
\(241\) 180.096 + 311.935i 0.747286 + 1.29434i 0.949119 + 0.314917i \(0.101977\pi\)
−0.201833 + 0.979420i \(0.564690\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 390.161 225.260i 1.59249 0.919427i
\(246\) 0 0
\(247\) 30.2122 52.3291i 0.122317 0.211859i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 400.179i 1.59434i −0.603755 0.797170i \(-0.706330\pi\)
0.603755 0.797170i \(-0.293670\pi\)
\(252\) 0 0
\(253\) 49.5857 0.195991
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −315.035 181.885i −1.22582 0.707725i −0.259664 0.965699i \(-0.583612\pi\)
−0.966152 + 0.257974i \(0.916945\pi\)
\(258\) 0 0
\(259\) −66.5755 115.312i −0.257048 0.445221i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 326.570 188.546i 1.24171 0.716903i 0.272270 0.962221i \(-0.412226\pi\)
0.969443 + 0.245318i \(0.0788923\pi\)
\(264\) 0 0
\(265\) −197.576 + 342.211i −0.745568 + 1.29136i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 170.849i 0.635125i −0.948237 0.317562i \(-0.897136\pi\)
0.948237 0.317562i \(-0.102864\pi\)
\(270\) 0 0
\(271\) −50.4041 −0.185993 −0.0929965 0.995666i \(-0.529645\pi\)
−0.0929965 + 0.995666i \(0.529645\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 137.202 + 79.2136i 0.498917 + 0.288050i
\(276\) 0 0
\(277\) 12.8031 + 22.1756i 0.0462204 + 0.0800561i 0.888210 0.459438i \(-0.151949\pi\)
−0.841990 + 0.539494i \(0.818616\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −290.267 + 167.586i −1.03298 + 0.596391i −0.917837 0.396958i \(-0.870066\pi\)
−0.115143 + 0.993349i \(0.536733\pi\)
\(282\) 0 0
\(283\) −7.48979 + 12.9727i −0.0264657 + 0.0458399i −0.878955 0.476905i \(-0.841759\pi\)
0.852489 + 0.522745i \(0.175092\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 509.834i 1.77643i
\(288\) 0 0
\(289\) 282.535 0.977629
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −261.015 150.697i −0.890837 0.514325i −0.0166210 0.999862i \(-0.505291\pi\)
−0.874216 + 0.485537i \(0.838624\pi\)
\(294\) 0 0
\(295\) −12.0051 20.7934i −0.0406953 0.0704863i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7.27755 4.20169i 0.0243396 0.0140525i
\(300\) 0 0
\(301\) 218.793 378.960i 0.726887 1.25900i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 160.124i 0.524997i
\(306\) 0 0
\(307\) 44.7469 0.145755 0.0728777 0.997341i \(-0.476782\pi\)
0.0728777 + 0.997341i \(0.476782\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −281.348 162.436i −0.904656 0.522303i −0.0259480 0.999663i \(-0.508260\pi\)
−0.878708 + 0.477360i \(0.841594\pi\)
\(312\) 0 0
\(313\) −156.894 271.748i −0.501258 0.868205i −0.999999 0.00145368i \(-0.999537\pi\)
0.498741 0.866751i \(-0.333796\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −47.9847 + 27.7040i −0.151371 + 0.0873942i −0.573773 0.819015i \(-0.694521\pi\)
0.422401 + 0.906409i \(0.361187\pi\)
\(318\) 0 0
\(319\) 125.793 217.880i 0.394335 0.683008i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 54.9119i 0.170006i
\(324\) 0 0
\(325\) 26.8490 0.0826123
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 744.802 + 430.012i 2.26384 + 1.30703i
\(330\) 0 0
\(331\) 7.70204 + 13.3403i 0.0232690 + 0.0403031i 0.877425 0.479713i \(-0.159259\pi\)
−0.854156 + 0.520016i \(0.825926\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −370.419 + 213.862i −1.10573 + 0.638393i
\(336\) 0 0
\(337\) −37.8837 + 65.6164i −0.112414 + 0.194708i −0.916743 0.399477i \(-0.869192\pi\)
0.804329 + 0.594184i \(0.202525\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 449.102i 1.31701i
\(342\) 0 0
\(343\) 841.949 2.45466
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 578.651 + 334.084i 1.66758 + 0.962779i 0.968936 + 0.247312i \(0.0795472\pi\)
0.698646 + 0.715467i \(0.253786\pi\)
\(348\) 0 0
\(349\) −123.015 213.069i −0.352479 0.610512i 0.634204 0.773166i \(-0.281328\pi\)
−0.986683 + 0.162654i \(0.947995\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −156.510 + 90.3612i −0.443372 + 0.255981i −0.705027 0.709181i \(-0.749065\pi\)
0.261655 + 0.965161i \(0.415732\pi\)
\(354\) 0 0
\(355\) −103.778 + 179.748i −0.292331 + 0.506332i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 256.273i 0.713852i 0.934133 + 0.356926i \(0.116175\pi\)
−0.934133 + 0.356926i \(0.883825\pi\)
\(360\) 0 0
\(361\) 105.384 0.291922
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −233.808 134.989i −0.640570 0.369833i
\(366\) 0 0
\(367\) −270.358 468.274i −0.736671 1.27595i −0.953986 0.299850i \(-0.903063\pi\)
0.217316 0.976101i \(-0.430270\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1115.88 + 644.252i −3.00776 + 1.73653i
\(372\) 0 0
\(373\) −85.9847 + 148.930i −0.230522 + 0.399276i −0.957962 0.286896i \(-0.907377\pi\)
0.727440 + 0.686171i \(0.240710\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 42.6367i 0.113095i
\(378\) 0 0
\(379\) 170.849 0.450789 0.225394 0.974268i \(-0.427633\pi\)
0.225394 + 0.974268i \(0.427633\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 505.681 + 291.955i 1.32031 + 0.762284i 0.983779 0.179386i \(-0.0574112\pi\)
0.336536 + 0.941671i \(0.390745\pi\)
\(384\) 0 0
\(385\) −414.641 718.179i −1.07699 1.86540i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −384.752 + 222.137i −0.989080 + 0.571045i −0.904999 0.425413i \(-0.860129\pi\)
−0.0840807 + 0.996459i \(0.526795\pi\)
\(390\) 0 0
\(391\) 3.81837 6.61361i 0.00976565 0.0169146i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 100.419i 0.254225i
\(396\) 0 0
\(397\) 575.090 1.44859 0.724294 0.689491i \(-0.242166\pi\)
0.724294 + 0.689491i \(0.242166\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −141.318 81.5902i −0.352415 0.203467i 0.313333 0.949643i \(-0.398554\pi\)
−0.665748 + 0.746176i \(0.731888\pi\)
\(402\) 0 0
\(403\) 38.0551 + 65.9134i 0.0944295 + 0.163557i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −148.757 + 85.8850i −0.365497 + 0.211020i
\(408\) 0 0
\(409\) 300.641 520.725i 0.735063 1.27317i −0.219633 0.975583i \(-0.570486\pi\)
0.954696 0.297584i \(-0.0961808\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 78.2922i 0.189570i
\(414\) 0 0
\(415\) −236.051 −0.568798
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −158.620 91.5795i −0.378569 0.218567i 0.298626 0.954370i \(-0.403472\pi\)
−0.677195 + 0.735803i \(0.736805\pi\)
\(420\) 0 0
\(421\) 83.7724 + 145.098i 0.198984 + 0.344651i 0.948199 0.317676i \(-0.102902\pi\)
−0.749215 + 0.662327i \(0.769569\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 21.1306 12.1998i 0.0497191 0.0287053i
\(426\) 0 0
\(427\) 261.065 452.178i 0.611394 1.05897i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 644.766i 1.49598i 0.663712 + 0.747988i \(0.268980\pi\)
−0.663712 + 0.747988i \(0.731020\pi\)
\(432\) 0 0
\(433\) 133.514 0.308347 0.154174 0.988044i \(-0.450729\pi\)
0.154174 + 0.988044i \(0.450729\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 56.1714 + 32.4306i 0.128539 + 0.0742119i
\(438\) 0 0
\(439\) 46.2276 + 80.0685i 0.105302 + 0.182388i 0.913862 0.406026i \(-0.133086\pi\)
−0.808560 + 0.588414i \(0.799752\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −150.157 + 86.6933i −0.338955 + 0.195696i −0.659810 0.751433i \(-0.729363\pi\)
0.320855 + 0.947128i \(0.396030\pi\)
\(444\) 0 0
\(445\) 14.9694 25.9277i 0.0336391 0.0582646i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 430.692i 0.959224i −0.877481 0.479612i \(-0.840777\pi\)
0.877481 0.479612i \(-0.159223\pi\)
\(450\) 0 0
\(451\) −657.706 −1.45833
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −121.711 70.2700i −0.267497 0.154440i
\(456\) 0 0
\(457\) 262.843 + 455.257i 0.575148 + 0.996186i 0.996025 + 0.0890687i \(0.0283891\pi\)
−0.420877 + 0.907118i \(0.638278\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.54999 0.894890i 0.00336224 0.00194119i −0.498318 0.866994i \(-0.666049\pi\)
0.501680 + 0.865053i \(0.332715\pi\)
\(462\) 0 0
\(463\) −263.166 + 455.817i −0.568394 + 0.984487i 0.428331 + 0.903622i \(0.359102\pi\)
−0.996725 + 0.0808651i \(0.974232\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 409.322i 0.876494i 0.898855 + 0.438247i \(0.144400\pi\)
−0.898855 + 0.438247i \(0.855600\pi\)
\(468\) 0 0
\(469\) −1394.72 −2.97381
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −488.873 282.251i −1.03356 0.596726i
\(474\) 0 0
\(475\) 103.616 + 179.469i 0.218140 + 0.377829i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −525.207 + 303.228i −1.09647 + 0.633045i −0.935290 0.353881i \(-0.884862\pi\)
−0.161175 + 0.986926i \(0.551528\pi\)
\(480\) 0 0
\(481\) −14.5551 + 25.2102i −0.0302601 + 0.0524120i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 397.991i 0.820600i
\(486\) 0 0
\(487\) −275.131 −0.564950 −0.282475 0.959275i \(-0.591155\pi\)
−0.282475 + 0.959275i \(0.591155\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −127.469 73.5945i −0.259612 0.149887i 0.364546 0.931186i \(-0.381224\pi\)
−0.624157 + 0.781299i \(0.714558\pi\)
\(492\) 0 0
\(493\) −19.3735 33.5558i −0.0392971 0.0680646i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −586.120 + 338.397i −1.17932 + 0.680879i
\(498\) 0 0
\(499\) 226.308 391.977i 0.453523 0.785526i −0.545079 0.838385i \(-0.683500\pi\)
0.998602 + 0.0528594i \(0.0168335\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 571.541i 1.13627i −0.822937 0.568133i \(-0.807666\pi\)
0.822937 0.568133i \(-0.192334\pi\)
\(504\) 0 0
\(505\) 5.42449 0.0107416
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 394.136 + 227.554i 0.774333 + 0.447062i 0.834418 0.551132i \(-0.185804\pi\)
−0.0600849 + 0.998193i \(0.519137\pi\)
\(510\) 0 0
\(511\) −440.171 762.399i −0.861392 1.49198i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5.38981 + 3.11181i −0.0104656 + 0.00604234i
\(516\) 0 0
\(517\) 554.732 960.823i 1.07298 1.85846i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 846.127i 1.62404i −0.583627 0.812022i \(-0.698367\pi\)
0.583627 0.812022i \(-0.301633\pi\)
\(522\) 0 0
\(523\) 487.616 0.932345 0.466172 0.884694i \(-0.345633\pi\)
0.466172 + 0.884694i \(0.345633\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 59.9000 + 34.5833i 0.113662 + 0.0656229i
\(528\) 0 0
\(529\) −259.990 450.316i −0.491474 0.851258i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −96.5296 + 55.7314i −0.181106 + 0.104562i
\(534\) 0 0
\(535\) −202.565 + 350.853i −0.378627 + 0.655801i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1895.13i 3.51601i
\(540\) 0 0
\(541\) −608.302 −1.12440 −0.562202 0.827000i \(-0.690045\pi\)
−0.562202 + 0.827000i \(0.690045\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 48.9592 + 28.2666i 0.0898334 + 0.0518653i
\(546\) 0 0
\(547\) −431.671 747.677i −0.789162 1.36687i −0.926481 0.376341i \(-0.877182\pi\)
0.137319 0.990527i \(-0.456151\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 285.000 164.545i 0.517241 0.298629i
\(552\) 0 0
\(553\) 163.722 283.576i 0.296062 0.512795i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 331.526i 0.595200i 0.954691 + 0.297600i \(0.0961861\pi\)
−0.954691 + 0.297600i \(0.903814\pi\)
\(558\) 0 0
\(559\) −95.6674 −0.171140
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 514.024 + 296.772i 0.913010 + 0.527126i 0.881398 0.472374i \(-0.156603\pi\)
0.0316114 + 0.999500i \(0.489936\pi\)
\(564\) 0 0
\(565\) −208.642 361.378i −0.369278 0.639608i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −889.155 + 513.354i −1.56266 + 0.902204i −0.565676 + 0.824627i \(0.691385\pi\)
−0.996986 + 0.0775764i \(0.975282\pi\)
\(570\) 0 0
\(571\) 191.843 332.282i 0.335977 0.581929i −0.647695 0.761900i \(-0.724267\pi\)
0.983672 + 0.179971i \(0.0576002\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 28.8204i 0.0501224i
\(576\) 0 0
\(577\) −777.433 −1.34737 −0.673685 0.739019i \(-0.735290\pi\)
−0.673685 + 0.739019i \(0.735290\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −666.591 384.856i −1.14732 0.662403i
\(582\) 0 0
\(583\) 831.110 + 1439.53i 1.42557 + 2.46917i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 581.520 335.741i 0.990665 0.571961i 0.0851921 0.996365i \(-0.472850\pi\)
0.905473 + 0.424404i \(0.139516\pi\)
\(588\) 0 0
\(589\) −293.727 + 508.749i −0.498687 + 0.863751i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 536.457i 0.904650i 0.891853 + 0.452325i \(0.149405\pi\)
−0.891853 + 0.452325i \(0.850595\pi\)
\(594\) 0 0
\(595\) −127.718 −0.214653
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 735.438 + 424.605i 1.22778 + 0.708857i 0.966564 0.256425i \(-0.0825446\pi\)
0.261212 + 0.965282i \(0.415878\pi\)
\(600\) 0 0
\(601\) −330.692 572.775i −0.550236 0.953037i −0.998257 0.0590138i \(-0.981204\pi\)
0.448021 0.894023i \(-0.352129\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −515.202 + 297.452i −0.851574 + 0.491656i
\(606\) 0 0
\(607\) 10.9541 18.9730i 0.0180463 0.0312570i −0.856861 0.515547i \(-0.827589\pi\)
0.874908 + 0.484290i \(0.160922\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 188.023i 0.307730i
\(612\) 0 0
\(613\) 1164.75 1.90008 0.950038 0.312133i \(-0.101044\pi\)
0.950038 + 0.312133i \(0.101044\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −558.227 322.292i −0.904743 0.522354i −0.0260071 0.999662i \(-0.508279\pi\)
−0.878736 + 0.477308i \(0.841613\pi\)
\(618\) 0 0
\(619\) 564.469 + 977.690i 0.911905 + 1.57947i 0.811370 + 0.584533i \(0.198722\pi\)
0.100535 + 0.994933i \(0.467944\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 84.5449 48.8120i 0.135706 0.0783499i
\(624\) 0 0
\(625\) 146.510 253.763i 0.234416 0.406021i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 26.4544i 0.0420579i
\(630\) 0 0
\(631\) 143.212 0.226961 0.113480 0.993540i \(-0.463800\pi\)
0.113480 + 0.993540i \(0.463800\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 625.343 + 361.042i 0.984792 + 0.568570i
\(636\) 0 0
\(637\) −160.586 278.143i −0.252097 0.436645i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 198.418 114.557i 0.309545 0.178716i −0.337178 0.941441i \(-0.609472\pi\)
0.646723 + 0.762725i \(0.276139\pi\)
\(642\) 0 0
\(643\) −554.682 + 960.737i −0.862646 + 1.49415i 0.00671893 + 0.999977i \(0.497861\pi\)
−0.869365 + 0.494170i \(0.835472\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1052.57i 1.62685i −0.581669 0.813426i \(-0.697600\pi\)
0.581669 0.813426i \(-0.302400\pi\)
\(648\) 0 0
\(649\) −101.000 −0.155624
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −795.499 459.282i −1.21822 0.703341i −0.253685 0.967287i \(-0.581643\pi\)
−0.964537 + 0.263946i \(0.914976\pi\)
\(654\) 0 0
\(655\) 207.772 + 359.872i 0.317210 + 0.549424i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −207.288 + 119.678i −0.314549 + 0.181605i −0.648960 0.760822i \(-0.724796\pi\)
0.334411 + 0.942427i \(0.391463\pi\)
\(660\) 0 0
\(661\) 177.793 307.946i 0.268976 0.465879i −0.699622 0.714513i \(-0.746648\pi\)
0.968598 + 0.248634i \(0.0799816\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1084.75i 1.63121i
\(666\) 0 0
\(667\) 45.7673 0.0686167
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −583.328 336.784i −0.869341 0.501914i
\(672\) 0 0
\(673\) 291.429 + 504.769i 0.433029 + 0.750028i 0.997132 0.0756758i \(-0.0241114\pi\)
−0.564103 + 0.825704i \(0.690778\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −154.450 + 89.1718i −0.228139 + 0.131716i −0.609713 0.792622i \(-0.708715\pi\)
0.381574 + 0.924338i \(0.375382\pi\)
\(678\) 0 0
\(679\) 648.883 1123.90i 0.955645 1.65522i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 660.510i 0.967072i 0.875325 + 0.483536i \(0.160648\pi\)
−0.875325 + 0.483536i \(0.839352\pi\)
\(684\) 0 0
\(685\) −749.080 −1.09355
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 243.959 + 140.850i 0.354077 + 0.204427i
\(690\) 0 0
\(691\) 43.2571 + 74.9236i 0.0626008 + 0.108428i 0.895627 0.444805i \(-0.146727\pi\)
−0.833026 + 0.553233i \(0.813394\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 322.834 186.388i 0.464509 0.268184i
\(696\) 0 0
\(697\) −50.6469 + 87.7231i −0.0726642 + 0.125858i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1204.11i 1.71770i −0.512227 0.858850i \(-0.671179\pi\)
0.512227 0.858850i \(-0.328821\pi\)
\(702\) 0 0
\(703\) −224.686 −0.319610
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 15.3184 + 8.84406i 0.0216667 + 0.0125093i
\(708\) 0 0
\(709\) −401.944 696.187i −0.566917 0.981928i −0.996869 0.0790766i \(-0.974803\pi\)
0.429952 0.902852i \(-0.358530\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −70.7531 + 40.8493i −0.0992329 + 0.0572921i
\(714\) 0 0
\(715\) −90.6510 + 157.012i −0.126785 + 0.219597i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 66.1101i 0.0919474i 0.998943 + 0.0459737i \(0.0146390\pi\)
−0.998943 + 0.0459737i \(0.985361\pi\)
\(720\) 0 0
\(721\) −20.2939 −0.0281469
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 126.637 + 73.1138i 0.174671 + 0.100847i
\(726\) 0 0
\(727\) −259.834 450.045i −0.357405 0.619044i 0.630121 0.776497i \(-0.283005\pi\)
−0.987527 + 0.157453i \(0.949672\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −75.2918 + 43.4698i −0.102998 + 0.0594662i
\(732\) 0 0
\(733\) −80.1459 + 138.817i −0.109340 + 0.189382i −0.915503 0.402311i \(-0.868207\pi\)
0.806163 + 0.591693i \(0.201540\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1799.24i 2.44130i
\(738\) 0 0
\(739\) 122.849 0.166237 0.0831184 0.996540i \(-0.473512\pi\)
0.0831184 + 0.996540i \(0.473512\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 585.944 + 338.295i 0.788619 + 0.455309i 0.839476 0.543397i \(-0.182862\pi\)
−0.0508572 + 0.998706i \(0.516195\pi\)
\(744\) 0 0
\(745\) −180.398 312.458i −0.242145 0.419407i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1144.06 + 660.523i −1.52745 + 0.881873i
\(750\) 0 0
\(751\) −171.430 + 296.925i −0.228268 + 0.395373i −0.957295 0.289113i \(-0.906640\pi\)
0.729027 + 0.684485i \(0.239973\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 64.4229i 0.0853283i
\(756\) 0 0
\(757\) 452.220 0.597385 0.298692 0.954349i \(-0.403450\pi\)
0.298692 + 0.954349i \(0.403450\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −203.520 117.503i −0.267438 0.154405i 0.360285 0.932842i \(-0.382680\pi\)
−0.627723 + 0.778437i \(0.716013\pi\)
\(762\) 0 0
\(763\) 92.1714 + 159.646i 0.120801 + 0.209234i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −14.8235 + 8.55834i −0.0193266 + 0.0111582i
\(768\) 0 0
\(769\) 318.439 551.552i 0.414095 0.717233i −0.581238 0.813733i \(-0.697432\pi\)
0.995333 + 0.0965005i \(0.0307649\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 592.885i 0.766992i 0.923543 + 0.383496i \(0.125280\pi\)
−0.923543 + 0.383496i \(0.874720\pi\)
\(774\) 0 0
\(775\) −261.029 −0.336811
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −745.059 430.160i −0.956430 0.552195i
\(780\) 0 0
\(781\) 436.545 + 756.118i 0.558956 + 0.968141i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 720.480 415.969i 0.917808 0.529897i
\(786\) 0 0
\(787\) −666.904 + 1155.11i −0.847400 + 1.46774i 0.0361199 + 0.999347i \(0.488500\pi\)
−0.883520 + 0.468393i \(0.844833\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1360.67i 1.72020i
\(792\) 0 0
\(793\) −114.151 −0.143948
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 638.540 + 368.661i 0.801179 + 0.462561i 0.843883 0.536527i \(-0.180264\pi\)
−0.0427041 + 0.999088i \(0.513597\pi\)
\(798\) 0 0
\(799\) −85.4347 147.977i −0.106927 0.185203i
\(800\) 0 0
\(801\) 0 0